Webster has been included in the Australian squad amid Mitchell Marsh's fitness concerns.
The second match of the ongoing Border-Gavaskar Trophy will be played with pink ball from December 6 to 10 at the Adelaide Oval.
Marsh suffered an injury setback during Australia’s 295-run thrashing at the hands of India in the series opener in Perth. Despite coach Andrew McDonald suggesting that there will be no changes in the squad, Webster has been included as cover.
Webster had a remarkable Sheffield Shield season last year, scoring over 900 runs and claiming 30 wickets. The all-rounder amassed 448 runs at an average of 56 and picked 16 wickets this summer.
Webster, 30, played in the two unofficial Tests between India A and Australia A earlier this month and impressed with his all-round performances.
“To get a few runs and wickets (for Australia A) was pleasing against a strong Indian side,” Webster said, as quoted by Cricbuzz.
“Any time you’re playing ‘A’ cricket, it’s the one step below Test level, so it does hold you in good stead.
“To get the call from ‘Bails’ (men’s selection chair George Bailey) at the end of the NSW game was a really proud moment and I can’t wait to get stuck in.
“There’s a tight turnaround between the Adelaide and Gabba Test so I think (I’m there) just to have some cover there for that middle-order role, whichever way they go,” he added.
Australia squad for second Test: Pat Cummins (c), Scott Boland, Alex Carey (wk), Josh Hazlewood, Travis Head, Josh Inglis, Usman Khawaja, Marnus Labuschagne, Nathan Lyon, Mitch Marsh, Nathan McSweeney, Steve Smith, Mitchell Starc, Beau Webster